Overview
An Exponential Moving Average gives recent samples more weight while retaining a fading memory of older samples.
CoreSource checked
Exponential Moving Average
Smooths a sequence by blending each new value with the previous smoothed value.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Signal Processing
- Difficulty
- Beginner
- Family
- Recursive Filter
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 2
- Code example
- Ready
- Visualization
- Ready
Core Concepts
recursive smoothingsmoothing factorstreaming statelow-pass behavior
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(1)
Average
O(n)
Worst
O(n)
Space
O(1)
When to Use
- Use when a streaming trend estimate is needed with constant memory.
- Use when metrics dashboards is a central requirement.
When Not to Use
- Avoid when a fixed finite window average is required for interpretability.
- Avoid when the sampling rate, window size, or stationarity assumptions do not hold.
What It Does
- Blends new samples with prior state
- Smooths short-term noise
- Responds faster than a long simple average
Use Cases
- Metrics dashboards
- Sensor smoothing
- Trend tracking
Inputs
- Signal samples
- Smoothing factor
Outputs
- Smoothed sequence
Key Formulas (1)
EMA update
emanext = α · sample + (1 − α) · emaprevious
ema_next = alpha * sample + (1 - alpha) * ema_previousBlends the latest sample with the previous smoothed value.
Pseudocode
- 1.Initialize the smoothed value
- 2.For each new sample, blend it with the previous smoothed value
- 3.Emit the updated smoothed value
Canonical Example
- Input
- previous = 10, sample = 14, alpha = 0.25
- Output
- next = 11
- Explanation
- The new estimate moves one quarter of the way from 10 to 14.
Implementation Notes
- Document whether alpha is configured directly or derived from a time constant.
- Plot or inspect both the original and processed signal for small test cases.
- Keep a tiny example with known output beside the implementation.
- Keep sampling rate, window size, latency, and boundary conventions explicit in tests.
Common Pitfalls
- Initialization can bias early values if not handled clearly.
- Boundary handling and phase response can change the result in visible or audible ways.
- Not defining boundary, empty, or degenerate inputs before implementation.
- Ignoring sampling rate, boundary handling, or phase behavior can make the output misleading.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow a noisy line and a smoother line that follows it with some lag.
Step 1 of 3: Initialize the smoothed value
signal-transformNotes
Smaller alpha values smooth more but react more slowly.
Sources (1)
What each reference supports for this entry.
Discrete-Time Signal Processing
BookSignal-processing reference for digital filters, convolution, spectral analysis, windows, resampling, and transform-based methods.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageVariant ofMoving Average
EMA replaces a fixed window with exponentially decaying weights.
Related Algorithms
Tags
Signal ProcessingFilteringSmoothingIterative